Distorted Wave Born Approximation Formalism Research Articles

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation.

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ2 = (2)2 and (71)2 Å2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of qz = 0.05 and 0.10 Å-1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both qz values simultaneously, that is, identical fitting parameters were applied at both values of qz. The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for qz = 0.04, 0.05, and 0.06 Å-1. Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of qz. Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

Various facets of magnetic charge correlation: Micromagnetic and distorted-wave Born approximation simulations study

The emergent concept of magnetic charge quasi-particle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. We report on the exploration of magnetic phases due to various magnetic charge correlation using the complementary numerical techniques of micromagnetic and distorted wave Born approximation simulations in artificial permalloy honeycomb lattice. The honeycomb element length varies between 10 nm and 100 nm, while the width and thickness are kept within the single domain limit. In addition to the charge ordered loop state, we observe disordered charge arrangement, characterized by the random distribution of $\pm$Q charges, in single domain size honeycomb lattice. As the length of honeycomb element increases, low multiplicity magnetic charges tend to form contiguous bands in thinner lattice. Thin honeycomb lattice with 100 nm element length exhibits a perfect spin ice pattern, which remains unaffected to the modest increase in the width of element size. We simulate scattering profiles under the pretext of distorted wave Born approximation formalism for the micromagnetic phases. The results are expected to provide useful guidance in the experimental investigation of magnetic phases in artificial honeycomb magnet.

Sensitivity of transfer cross sections to the bound-state wave functions

We test the sensitivity of transfer reactions to the bound state wave functions within a distorted wave Born approximation formalism. Using supersymmetric transformations, we remove the Pauli-forbidden states from the two-body potentials and generate an equivalent supersymmetric partner. Wave functions from these potentials have the same asymptotics, but they differ in the nuclear interior. This allows us to study the influence of the nuclear interior on transfer cross sections. We apply the calculations to the O16(d,p)17O and C12(7Li, t)16O reactions, which are typical examples of nucleon and α transfer, respectively. The spectroscopic factors for 17O are decreased by about 30% when using supersymmetric potentials. For 16O, the differences are smaller. However, we show that ambiguities exist in the determination of the spectroscopic factors, due to the choice of the angular range where the fit is performed.

Neutron transfer in reaction 18O + 181Ta with formation of neutron-rich oxygen isotopes

Differential cross sections for the formation of oxygen isotopes in the reaction 18O + 181Ta have been measured at projectile nucleus energy 10 A⋅MeV on the high-resolution magnetic spectrometer MAVR. Theoretical analysis of product yields has been performed in the finite-range distorted-wave Born approximation formalism using the FRESCO code under the assumption of sequential neutron transfer mechanism. The results of calculations are in good agreement with experimental data.

Projectile charge effects on the differential cross sections for the ionization of molecular nitrogen by positrons and electrons

Triple differential cross sections (TDCSs) are reported for the positron and electron impact ionization of molecular nitrogen at a projectile energy of 250 eV. The TDCSs are calculated in the distorted wave Born approximation formalism using the orientation-averaged molecular orbitals. The present attempt is helpful for analyzing recent measurements (de Lucio and DuBois 2016 Phys. Rev. A 93 032710) and studying the effect of projectile charge on the ionization of a molecular target. The TDCS trends are compared for positron and electron impact ionization in terms of binary and recoil intensities and binary lobe positions for different values of energy loss. The binary emission of electrons is enhanced for positron impact; however, nearly the same recoil emission is observed for positrons as well as electron impact. Significant discrepancies are observed in the measurements in terms of the relative binary intensity for positron and electron impact.

Electron impact differential cross sections of Kr (4p) atoms for the perpendicular plane emission of final state electrons

The perpendicular plane ionization results of (e, 2e) triple differential cross sections (TDCS) for the Kr (4p) atoms are reported at the incident electron energies 2eV–50eV above ionization potential. Modified distorted wave Born approximation formalism has been employed to calculate the TDCS. The results of our calculations have been compared with the measurements of Nixon et al. and it is observed that there are certain discrepancies between theoretical and experimental results which indicate that further theoretical efforts are required to understand the cross section trends of krypton atoms in the perpendicular plane ionization.

Coincident excitation and radiative decay in electron-nucleus collisions

The distorted-wave Born approximation formalism for the description of the $(e,{e}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction, in which emitted photons and scattered electrons are simultaneously detected, is outlined. Both the Coulomb and the magnetic scattering are fully taken into account. The influence of electron bremsstrahlung is estimated within the plane-wave Born approximation. Recoil effects are also discussed. The formalism is applied for the low-energy $(e,{e}^{\ensuremath{'}}\ensuremath{\gamma})^{92}\mathrm{Zr}$ reaction with excitation of the first collective (${2}_{1}^{+}$) and mixed-symmetry (${2}_{2}^{+}$) states. The corresponding transition charge and current densities are taken from a random-phase approximation (RPA) calculation within the quasiparticle phonon model. It is shown, by this example, in which way the magnetic subshell population of the excited state influences the angular distribution of the decay photon. For these quadrupole excitations the influence of magnetic scattering is only prominent at the backmost scattering angles, where a clear distinction of the photon pattern pertaining to the two states is predicted.

Fully differential cross sections for low to intermediate energy perpendicular plane ionization of xenon atoms

Triple differential cross section (TDCS) results are reported for the perpendicular plane ionization of Xe (5p) at incident electron energies 5eV, 10eV, 20eV, and 40eV above ionization potential. The modified distorted wave Born approximation formalism with first as well as the second order Born terms has been used to calculate the TDCS. Effects of target polarization and post collision interaction have also been included. We compare the (e, 2e) TDCS results of our calculation with the recent available experimental data and theoretical results and discuss the process contributing to structure seen in the differential cross section. It has been observed from the present study that the second order effect and target polarization make significant contribution in description of collision dynamics of xenon at the low and intermediate energy for the perpendicular emission of electrons.

Capture cross-section and rate of the 1 4 C(n, γ) 1 5 C reaction from the Coulomb dissociation of 1 5 C

We calculate the Coulomb dissociation of 15C on a Pb target at 68 MeV/u incident beam energy within the fully quantum mechanical distorted wave Born approximation formalism of breakup reactions. The capture cross-section and the subsequently rate of the 14C(n, γ) 15C reaction are calculated from the photodisintegration of 15C, using the principle of detailed balance. Our theoretical model is free from the uncertainties associated with the multipole strength distributions of the projectile.

Determination of subshell-resolvedL-shell-ionization cross sections of gold induced by 15–40-keV electrons

The $L$-subshell specific electron impact ionization cross sections, near the ionization threshold ($15<E<40$ keV) of gold are calculated from the measured production cross sections in this collaborative work between an experimental and a theoretical group. Calculations are performed using the distorted wave Born approximation formalism, and the modified relativistic binary encounter Bethe model to understand the data. The observed agreements and discrepancies between the two theoretical formalisms considered and the experimental data are reported.

Calculation of (e, 2e) triple differential cross sections of Mg in coplanar geometry

We report the results of triple differential cross section of coplanar (e, 2e) processes on Mg (3s) atom in modified distorted wave Born approximation (DWBA). The standard DWBA formalism has been modified by including the correlation-polarization potential (which is function of electron density) and post collision interaction. We compare our computed results with the available experimental data and observe that the inclusion of polarization potential in the standard DWBA is able to improve the agreement with experimental results.

(e, 2e) processes on Ne, Ar and Xe targets

Recently, there have been several attempts to explain the features of triple differential cross section (TDCS) for the (e, 2e) processes on inert targets Ne, Ar and Xe but there are still certain discrepancies in theoretical results and measurements, which require more theoretical efforts to understand the collision dynamics of these targets. We present in this paper the results of our modified distorted wave Born approximation (DWBA) calculation of TDCS for the ionization of Ne (2p), Ar (3p) and Xe (5p) targets. We modify the standard DWBA formalism by including the correlation-polarization potential (which is function of electron density) and compare our computed results with the available experimental and theoretical data. We observe that the polarization potential is able to improve the agreement with experimental results.

(e, 2e) triple differential cross sections of Ca atoms at low energies

Recently, several theoretical studies (Hitawala et al 2008 J. Phys. B: At. Mol. Opt. Phys.41 035205; Khajuria and Deshmukh 2008 Phys. Rev. A 78 024702; Chauhan et al 2005 Phys. Rev. A 71 032708) have been reported to analyze the measurements of triple differential cross section (TDCS) for (e, 2e) processes on Ca (4s2) atom in coplanar geometry (Murray 2005 Phys. Rev. A 72 062711). In this paper, the (e, 2e) TDCS of the Ca atom has been revisited with the inclusion of correlation-polarization potential and post-collision interaction in the distorted wave Born approximation formalism. We note that the present attempt significantly improves the understanding of (e, 2e) processes at low energies on Ca atom. Still there are several discrepancies between the experimental and theoretical results that require more theoretical attempts to explain them properly.

Importance of polarization effects in electron impact single ionization of argon atom

We report the results of our calculations of triple differential cross section (TDCS) for electron impact single ionization (i.e. (e, 2e) processes) from the 3s shell of argon using a modified distorted wave Born approximation formalism by including correlation–polarization potential, which accounts for both correlation and polarization effects. We observe that DWBA formalism including polarization potential is able to reproduce most of the trends of experimental data and hence provide a fututre direction for further investigation of ionization process from the 3s shell of argon. We also compare our results with the available theoretical and experimental results. The present calculations significantly improve the agreement with the experimental results but still there are certain discrepancies, which is a matter of further investigation.

X-ray dynamical diffraction from multilayer Laue lenses with rough interfaces

A modeling approach for x-ray dynamical diffraction from multilayer Laue lenses (MLLs) with rough interfaces is developed. Although still based on the principle of the distorted-wave Born approximation (DWBA), this model is formulated from the perspective of the physical scattering process, very different from the conventional DWBA formalism. Using this model, one can study x-ray scattering from rough interfaces in the regime of Fresnel diffraction and in the case of absorptive samples, for example, x-ray dynamical diffraction from MLLs with rough interfaces, which is hard to handle in the framework of the conventional DWBA. Theoretical simulations for various MLLs with rough interfaces are conducted. It is found that interfacial roughness results in a decrease in the local diffraction intensity, where the attenuation factor is a function of the root-mean-square (rms) roughness versus the local zone width ratio. This study shows that if all zones possess an identical rms roughness value that is less than half of the outmost MLL zone width, the focal broadening effect due to roughness is almost unnoticeable, provided that the mean position of the interface does not deviate from the required zone plate law. A further study shows that uncorrelated interfacial roughness can be treated themore » same as interfacial diffusion, in which case a roughness factor similar to the ''Debye-Waller factor'' can be used, and the pseudo-Fourier coefficients of the susceptibility function for an MLL [H. F. Yan et al., Phys. Rev. B 76, 115438 (2007)] have to be multiplied by this factor.« less

Coulomb dissociation ofLi9and the rate of the8Li(n,γ)9Lireaction

We calculate the Coulomb dissociation of $^{9}\mathrm{Li}$ on Pb and U targets at 28.5 MeV/A beam energy within a finite range distorted wave Born approximation formalism of the breakup reactions. Invoking the principle of detailed balance, these cross sections are used to determine the excitation function and subsequently the rate of the radiative capture reaction ${}^{8}\mathrm{Li}(n,\ensuremath{\gamma}){}^{9}\mathrm{Li}$ at astrophysical energies. Our method is free from the uncertainties associated with the multipole strength distributions of the $^{9}\mathrm{Li}$ nucleus. The rate of this reaction at a temperature of 10 K is found to be about 2900 ${\mathrm{cm}}^{3}$ ${\mathrm{mole}}^{\ensuremath{-}1}$ ${\mathrm{s}}^{\ensuremath{-}1}$.

(e, 2e) triple differential cross sections of alkali and alkali earth atoms: Na, K and Mg, Ca

Recently low-energy measurements have been reported for alkali targets Na and K and alkali earth targets Mg and Ca in coplanar symmetric geometry. We report the results of our calculation of triple differential cross section (TDCS) for electron impact single ionization (i.e. (e, 2e) processes) of alkali atoms Na, K and alkali earth atoms Mg, Ca in coplanar symmetric geometry. We have performed the present calculations using the distorted-wave Born approximation (DWBA) formalism at intermediate incident electron energies used in the recently performed experiments. Ionization takes place from the valence shell for all the targets investigated and the outgoing electrons share the excess energy equally. We have also considered the effect of target polarization in our DWBA calculations which may be an important quantity at incident electron energies used in the present investigation. We find that the DWBA formalism is able to reproduce most of the trend of experimental data and may provide a future direction for further investigation of ionization process on alkali and alkali earth metals. It is also observed that the second-order effects are more important to understand the collision dynamics of (e, 2e) processes on alkali earth targets

Coulomb-nuclear interference in the breakup of11Be

Within a theory of breakup reactions formulated in the framework of the post form distorted wave Born approximation, we calculate contributions of the pure Coulomb and the pure nuclear breakup as well as those of their interference terms to a variety of cross sections in breakup reactions of the one-neutron halo nucleus $^{11}$Be on a number of target nuclei. In contrast to the assumption often made, the Coulomb-nuclear interference terms are found to be non-negligible in case of exclusive cross sections of the fragments emitted in this reaction on medium mass and heavy target nuclei. The consideration of the nuclear breakup leads to a better description of such data.

Spin-polarized low-energy (e, 2e) spectroscopy of non-magnetic surfaces

For spin-polarized low-energy electrons impinging on non-magnetic crystalline surfaces, the collision with a valence electron and the ensuing emission of an electron pair are treated in a distorted-wave Born approximation formalism with exchange, in which the four relevant quasi-one-electron states are solutions of the Dirac equation. Numerical calculations for W(001), which were carried out in two coplanar geometries with normal and grazing incidence of a primary beam polarized normal to the reaction plane, show that the (e, 2e) cross section changes significantly upon reversal of the polarization. Originating mainly from spin-orbit coupling in the valence electron state, asymmetries of up to 30% occur in conjunction with sizable intensity. The calculated spectra respond sensitively to changes in the surface structure.

Quantitative study of interface roughness replication in multilayers using x-ray reflectivity and transmission electron microscopy

The recently appeared distorted wave Born approximation formalism is used for quantitative determination of interface roughness replication and lateral correlation length in periodical multilayered structures. The results obtained from x-ray diffraction are in very good agreement with analysis of cross-section transmission electron micrographs. We interpret transparently the obtained parameters and demonstrate the ability of the low-angle x-ray diffraction methodology for nondestructive and quantitative studying of interface roughness in magnetic multilayers.